Nintendo doesn't really compete in any of the genres that Sony relies on either.
Switch doesn't have a a single FPS, violent third person action games, racing sim, sports game, etc. that would really threaten Sony.
It's a platform largely driven by Nintendo mascot games, and Sony is no longer really interested in those types of games. They've given Crash Bandicoot a token remaster and that's it, but they kinda stopped making things like Crash and Spyro generations ago.
So that in part too is part of the reason I don't think Sony cares much. If tomorrow Nintendo stared to make FPS and racers ... then Sony's tune would probably change but so long as Nintendo stays in their bubble making Mario/Kirby/Pokemon/Donkey Kong/Yoshi/Animal Crossing etc. games as like 90% of their output ... I don't think Sony views them as a threat. Zelda, ok is maybe the one Nintendo franchise that kinda overlaps into Playstation territory and even that only kinda (and when Nintendo uses a more realistic art style). Metroid is small potatoes.
In the 90s there was far more overlap. Nintendo published games like GoldenEye, Perfect Dark, Zelda, Starcraft 64, Conker's Bad Fur Day, Star Wars Rogue Squadron, 1080 Snowboarding, NBA Courtside, Ken Griffey MLB, that certainly were right in the same wheel house Sony was targetting and Sony conversely used to make games like Crash Bandicoot, PaRappa the Rapper, and Spyro the Dragon that were aimed at the Nintendo mascot crowd. I guess they had Litte Big Planet but it looks like they've given up on that IP.